function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
n=size(theta);
theta1=theta(2:n,:);
X1=X(:,2:n);
J=(-(y'*log(sigmoid(X*theta))+(1-y)'*log(1-sigmoid(X*theta)))+theta1'*theta1*lambda/2)/m;
theta1=[0;theta1];
grad=(X'*(sigmoid(X*theta)-y)+lambda*theta1)/m;

% =============================================================

end
